Improved branch-cut-and-price for capacitated vehicle routing
The best performing exact algorithms for the capacitated vehicle routing problem developed in the last 10 years are based in the combination of cut and column generation. Some authors only used cuts expressed over the variables of the original formulation, in order to keep the pricing subproblem rel...
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| Vydané v: | Mathematical programming computation Ročník 9; číslo 1; s. 61 - 100 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2017
Springer Nature B.V |
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| ISSN: | 1867-2949, 1867-2957 |
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| Abstract | The best performing exact algorithms for the capacitated vehicle routing problem developed in the last 10 years are based in the combination of cut and column generation. Some authors only used cuts expressed over the variables of the original formulation, in order to keep the pricing subproblem relatively easy. Other authors could reduce the duality gaps by also using a restricted number of cuts over the master LP variables, stopping when the pricing becomes prohibitively hard. A particularly effective family of such cuts are the subset row cuts. This work introduces a technique for greatly reducing the impact on the pricing of these cuts, thus allowing much more cuts to be added. The newly proposed branch-cut-and-price algorithm also incorporates and combines for the first time (often in an improved way) several elements found in previous works, like route enumeration and strong branching. All the instances used for benchmarking exact algorithms, with up to 199 customers, were solved to optimality. Moreover, some larger instances with up to 360 customers, only considered before by heuristic methods, were solved too. |
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| AbstractList | The best performing exact algorithms for the capacitated vehicle routing problem developed in the last 10 years are based in the combination of cut and column generation. Some authors only used cuts expressed over the variables of the original formulation, in order to keep the pricing subproblem relatively easy. Other authors could reduce the duality gaps by also using a restricted number of cuts over the master LP variables, stopping when the pricing becomes prohibitively hard. A particularly effective family of such cuts are the subset row cuts. This work introduces a technique for greatly reducing the impact on the pricing of these cuts, thus allowing much more cuts to be added. The newly proposed branch-cut-and-price algorithm also incorporates and combines for the first time (often in an improved way) several elements found in previous works, like route enumeration and strong branching. All the instances used for benchmarking exact algorithms, with up to 199 customers, were solved to optimality. Moreover, some larger instances with up to 360 customers, only considered before by heuristic methods, were solved too. |
| Author | Pessoa, Artur Uchoa, Eduardo Pecin, Diego Poggi, Marcus |
| Author_xml | – sequence: 1 givenname: Diego surname: Pecin fullname: Pecin, Diego organization: Departamento de Informática, Pontifícia Universidade Católica do Rio de Janeiro – sequence: 2 givenname: Artur surname: Pessoa fullname: Pessoa, Artur organization: Departamento de Engenharia de Produção, Universidade Federal Fluminense – sequence: 3 givenname: Marcus surname: Poggi fullname: Poggi, Marcus organization: Departamento de Informática, Pontifícia Universidade Católica do Rio de Janeiro – sequence: 4 givenname: Eduardo surname: Uchoa fullname: Uchoa, Eduardo email: uchoa@producao.uff.br organization: Departamento de Engenharia de Produção, Universidade Federal Fluminense |
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| SubjectTerms | Algorithms Customers Enumeration Full Length Paper Heuristic methods Mathematics Mathematics and Statistics Mathematics of Computing Operations Research/Decision Theory Optimization Pricing Route planning Routing Theory of Computation Vehicle routing |
| Title | Improved branch-cut-and-price for capacitated vehicle routing |
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